{
  "id": 4671,
  "curve_key": "-5126978624:-961493597309440",
  "ainvs": [
    "0",
    "1",
    "0",
    "106812055",
    "1112875415719"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 68.99901804374133,
  "faltings_height": 3.8224513139234984,
  "conductor": "148797332771970176",
  "bad_primes": [
    "2",
    "7",
    "17",
    "41",
    "79",
    "103",
    "167",
    "271",
    "647"
  ],
  "discriminant": "-612984511215390704222199808",
  "regulator": "34395130.0477348701786762358979015335736246533222152985",
  "points": [
    [
      "-45014/9",
      "18183599/27"
    ],
    [
      "178674",
      "-75659033"
    ],
    [
      "69642",
      "18609691"
    ],
    [
      "72141/4",
      "-23874221/8"
    ],
    [
      "136554",
      "50616587"
    ],
    [
      "30162",
      "5636951"
    ],
    [
      "906741/4",
      "-864365521/8"
    ],
    [
      "-728646/121",
      "667272223/1331"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "I obtained this curve as a rational 2-isogenous partner of curve #4651: https://elliptic-rank.icarm.cloud/curve/4651. The source curve appears in Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I transported eight supplied independent rational points through the isogeny and checked them exactly on this minimal model. Same rank and conductor; rational torsion Z/2Z. Source-attributed isogeny construction.",
  "created_at": "2026-10-20 20:17:22",
  "updated_at": "2026-10-20 20:17:22"
}